My job needs me ________ even on weekends.

The right answer is: To work. (infinitive)

Infinitive:
- An infinitive is the word “to” + a verb’s root.

- We use the to-infinitive after certain verbs (verbs followed by to-infinitive), particularly verbs of thinking and feeling:

- Similar verbs like this:
Choose, decide, forget , expect, hope, hate, intend, learn, like, love, mean, plan, prefer, remember, want, would like/love etc.
Example: They decided to start a business together.

- Some verbs are followed by a direct object and then the to-infinitive: for example:
Example: He encouraged his friends to vote for him.

Source: British Council Learning website.